- In a saucepan, bring the water and butter to a boil. Remove from the heat. Add the flour at once and stir vigorously with wooden spoon until the dough forms a ball and pulls away from the pan.
- Remove from the heat and let cool for a few minutes. Add the eggs, one at a time, beating vigorously after each addition until smooth.
- Preheat the oven to 190 °C (375 °F). Butter a baking sheet and line with parchment paper.
- With a pastry bag filled with the choux dough, form 7.5-cm (3-inch) long éclairs on the baking sheet.
- Bake in the middle of the oven until lightly browned, about 30 minutes. Slice open the pastries horizontally so that the steam can escape, then return to the oven for a few minutes to dry slightly. Remove from the oven and let cool for 5 minutes.
- In a saucepan off the heat, whisk together the sugar, vanilla and eggs until light and fluffy. Add the flour and whisk until smooth. Add the hot milk and white chocolate. Stir over low heat until it thickens.
- Remove from the heat and cover with plastic wrap. Refrigerate.
- With a pastry bag, fill the éclairs. With a spoon, drizzle the melted semi-sweet chocolate over the éclairs. Keep refrigerated.